“Central to all of the goals of cluster analysis is the notion of the degree of similarity (or dissimilarity) between the individual objects being clustered.” (Elements of Statistical Learning)
This exploratory analysis will only be run on the complete case data for JH and SWS subscales.
First, we can check the pairwise correlation between the scales. In the plot below, the upper triangles provide the pearson correlation values. The lower triangles show the bivariate scatter plots. The diagonal shows a simple histogram and density plot of the univariate scale data.
JH has the highest pairwise correlation with SWS strength (0.48. Several of the SWS subscales correlate at a moderate or high level with other SWS subscales. We will see the effect of this when we look at item-specific PCA and cluster analysis later.
We want to examine how the items cluster when an unsupervised approach is taken. To do so, we will run a PCA analysis of the items.
Because John Henryism is scored on a scale with a different range than SWS, we’ll center and scale each of the items before applying PCA.
| PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 | PC10 | PC11 | PC12 | PC13 | PC14 | PC15 | PC16 | PC17 | PC18 | PC19 | PC20 | PC21 | PC22 | PC23 | PC24 | PC25 | PC26 | PC27 | PC28 | PC29 | PC30 | PC31 | PC32 | PC33 | PC34 | PC35 | PC36 | PC37 | PC38 | PC39 | PC40 | PC41 | PC42 | PC43 | PC44 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Standard deviation | 5.156 | 3.613 | 2.919 | 2.852 | 2.567 | 2.474 | 2.395 | 2.298 | 2.141 | 2.079 | 2.013 | 1.959 | 1.915 | 1.879 | 1.830 | 1.793 | 1.745 | 1.691 | 1.656 | 1.569 | 1.539 | 1.504 | 1.466 | 1.461 | 1.417 | 1.331 | 1.305 | 1.276 | 1.219 | 1.186 | 1.169 | 1.148 | 1.072 | 1.060 | 1.023 | 1.014 | 0.943 | 0.933 | 0.887 | 0.844 | 0.821 | 0.802 | 0.719 | 0 |
| Proportion of Variance | 0.174 | 0.085 | 0.056 | 0.053 | 0.043 | 0.040 | 0.038 | 0.035 | 0.030 | 0.028 | 0.027 | 0.025 | 0.024 | 0.023 | 0.022 | 0.021 | 0.020 | 0.019 | 0.018 | 0.016 | 0.016 | 0.015 | 0.014 | 0.014 | 0.013 | 0.012 | 0.011 | 0.011 | 0.010 | 0.009 | 0.009 | 0.009 | 0.008 | 0.007 | 0.007 | 0.007 | 0.006 | 0.006 | 0.005 | 0.005 | 0.004 | 0.004 | 0.003 | 0 |
| Cumulative Proportion | 0.174 | 0.260 | 0.315 | 0.369 | 0.412 | 0.452 | 0.489 | 0.524 | 0.554 | 0.582 | 0.609 | 0.634 | 0.658 | 0.681 | 0.703 | 0.724 | 0.744 | 0.763 | 0.781 | 0.797 | 0.812 | 0.827 | 0.841 | 0.855 | 0.868 | 0.880 | 0.891 | 0.902 | 0.911 | 0.921 | 0.930 | 0.938 | 0.946 | 0.953 | 0.960 | 0.967 | 0.972 | 0.978 | 0.983 | 0.988 | 0.992 | 0.997 | 1.000 | 1 |
Note that the first principle component (x-axis) nearly completely separates the John Henryism items from the SWS items. Some of the SWS strength items do tend to cluster with the JH items, when compressed to two dimensions.
The addition of a second principle component (y-axis) shows somewhat distinct clustering of SWS subscales.
Before I could begin with my cluster analysis, I build a pairwise distance matrix based on the centered and standardized data.
Next, I complete a k-means clustering, where \(k=6\), which is the number of scales we expect to observe.
For the k-means clustering, it does appear that JH separates out cleanly, but SWS is a bit more difficult to separate out.
| Item | assigned.cluster | scale |
|---|---|---|
| SWS5 | 1 | SWS emotion |
| SWS6 | ||
| SWS7 | ||
| SWS8 | ||
| SWS9 | ||
| SWS10 | ||
| SWS30 | ||
| SWS11 | 2 | SWS vulnerable |
| SWS12 | ||
| SWS13 | ||
| SWS14 | ||
| SWS15 | ||
| SWS21 | 3 | SWS care |
| SWS22 | ||
| SWS23 | ||
| SWS24 | ||
| SWS25 | ||
| SWS34 | ||
| SWS1 | 4 | SWS strength |
| SWS2 | ||
| SWS3 | ||
| SWS4 | ||
| JH_1 | JH | |
| JH_2 | ||
| JH_3 | ||
| JH_4 | ||
| JH_5 | ||
| JH_6 | ||
| JH_7 | ||
| JH_8 | ||
| JH_9 | ||
| JH_10 | ||
| JH_11 | ||
| JH_12 | ||
| SWS16 | 5 | SWS vulnerable |
| SWS31 | ||
| SWS17 | SWS succeed | |
| SWS18 | ||
| SWS32 | ||
| SWS33 | ||
| SWS29 | 6 | SWS strength |
| SWS35 | ||
| SWS19 | SWS succeed | |
| SWS20 |
“Intuitively, the larger the silhouette widths, the better the clustering. Specifically, observations with large silhouette widths (almost one) are well clustered, those with silhouette widths around zero tend to lie between clusters, and those with negative silhouette widths are likely placed in the wrong cluster.” (Sandrine Dudoit’s PH C240C/STAT C245C course notes)
| Item | assigned.cluster | scale |
|---|---|---|
| SWS1 | 1 | SWS strength |
| SWS2 | SWS strength | |
| SWS3 | SWS strength | |
| SWS4 | SWS strength | |
| SWS29 | 2 | SWS strength |
| SWS16 | SWS vulnerable | |
| SWS17 | SWS succeed | |
| SWS18 | SWS succeed | |
| SWS32 | SWS succeed | |
| SWS33 | SWS succeed | |
| JH_10 | JH | |
| SWS35 | 3 | SWS strength |
| SWS19 | SWS succeed | |
| SWS20 | SWS succeed | |
| SWS21 | SWS care | |
| SWS22 | SWS care | |
| SWS23 | SWS care | |
| SWS24 | SWS care | |
| SWS25 | SWS care | |
| SWS34 | SWS care | |
| SWS5 | 4 | SWS emotion |
| SWS6 | SWS emotion | |
| SWS7 | SWS emotion | |
| SWS8 | SWS emotion | |
| SWS9 | SWS emotion | |
| SWS10 | SWS emotion | |
| SWS30 | SWS emotion | |
| SWS11 | 5 | SWS vulnerable |
| SWS12 | SWS vulnerable | |
| SWS13 | SWS vulnerable | |
| SWS14 | SWS vulnerable | |
| SWS15 | SWS vulnerable | |
| SWS31 | SWS vulnerable | |
| JH_1 | 6 | JH |
| JH_2 | JH | |
| JH_3 | JH | |
| JH_4 | JH | |
| JH_5 | JH | |
| JH_6 | JH | |
| JH_7 | JH | |
| JH_8 | JH | |
| JH_9 | JH | |
| JH_11 | JH | |
| JH_12 | JH |
One approach is to pick the k that maximizes the silhouette width
K-modes is a more appropriate clustering method for use when the data is categorical.
| item | cluster | scale |
|---|---|---|
| JH_1 | 1 | JH |
| JH_2 | 1 | JH |
| JH_3 | 1 | JH |
| JH_4 | 1 | JH |
| JH_5 | 1 | JH |
| JH_6 | 1 | JH |
| JH_7 | 1 | JH |
| JH_8 | 1 | JH |
| JH_9 | 1 | JH |
| JH_10 | 1 | JH |
| JH_11 | 1 | JH |
| JH_12 | 1 | JH |
| SWS1 | 1 | SWS strength |
| SWS2 | 1 | SWS strength |
| SWS3 | 1 | SWS strength |
| SWS4 | 1 | SWS strength |
| item | cluster | scale |
|---|---|---|
| SWS21 | 2 | SWS care |
| SWS22 | 2 | SWS care |
| SWS23 | 2 | SWS care |
| SWS24 | 2 | SWS care |
| SWS25 | 2 | SWS care |
| SWS34 | 2 | SWS care |
| SWS5 | 2 | SWS emotion |
| SWS6 | 2 | SWS emotion |
| SWS7 | 2 | SWS emotion |
| SWS8 | 2 | SWS emotion |
| SWS9 | 2 | SWS emotion |
| SWS10 | 2 | SWS emotion |
| SWS30 | 2 | SWS emotion |
| SWS29 | 2 | SWS strength |
| SWS35 | 2 | SWS strength |
| SWS17 | 2 | SWS succeed |
| SWS18 | 2 | SWS succeed |
| SWS19 | 2 | SWS succeed |
| SWS20 | 2 | SWS succeed |
| SWS32 | 2 | SWS succeed |
| SWS33 | 2 | SWS succeed |
| SWS11 | 2 | SWS vulnerable |
| SWS12 | 2 | SWS vulnerable |
| SWS13 | 2 | SWS vulnerable |
| SWS14 | 2 | SWS vulnerable |
| SWS15 | 2 | SWS vulnerable |
| SWS16 | 2 | SWS vulnerable |
| SWS31 | 2 | SWS vulnerable |
| item | cluster | scale |
|---|---|---|
| SWS5 | 1 | SWS emotion |
| SWS1 | 1 | SWS strength |
| SWS2 | 1 | SWS strength |
| SWS3 | 1 | SWS strength |
| SWS4 | 1 | SWS strength |
| SWS29 | 1 | SWS strength |
| SWS35 | 1 | SWS strength |
| SWS17 | 1 | SWS succeed |
| SWS18 | 1 | SWS succeed |
| SWS20 | 1 | SWS succeed |
| SWS32 | 1 | SWS succeed |
| SWS16 | 1 | SWS vulnerable |
| SWS31 | 1 | SWS vulnerable |
| item | cluster | scale |
|---|---|---|
| JH_12 | 2 | JH |
| item | cluster | scale |
|---|---|---|
| SWS21 | 3 | SWS care |
| SWS22 | 3 | SWS care |
| SWS23 | 3 | SWS care |
| SWS24 | 3 | SWS care |
| SWS25 | 3 | SWS care |
| SWS34 | 3 | SWS care |
| SWS19 | 3 | SWS succeed |
| SWS33 | 3 | SWS succeed |
| item | cluster | scale |
|---|---|---|
| JH_1 | 4 | JH |
| JH_2 | 4 | JH |
| JH_3 | 4 | JH |
| JH_5 | 4 | JH |
| JH_6 | 4 | JH |
| item | cluster | scale |
|---|---|---|
| SWS6 | 5 | SWS emotion |
| SWS7 | 5 | SWS emotion |
| SWS8 | 5 | SWS emotion |
| SWS9 | 5 | SWS emotion |
| SWS10 | 5 | SWS emotion |
| SWS30 | 5 | SWS emotion |
| SWS11 | 5 | SWS vulnerable |
| SWS12 | 5 | SWS vulnerable |
| SWS13 | 5 | SWS vulnerable |
| SWS14 | 5 | SWS vulnerable |
| SWS15 | 5 | SWS vulnerable |
| item | cluster | scale |
|---|---|---|
| JH_4 | 6 | JH |
| JH_7 | 6 | JH |
| JH_8 | 6 | JH |
| JH_9 | 6 | JH |
| JH_10 | 6 | JH |
| JH_11 | 6 | JH |
Gini impurity: the measure of impurity in a node. 0 or 1 is best. 0.5 is worst.
\[I_G(n) = 1 - \sum_{i=1}^J (p_i)^2\]
where \(J\) is the number of classes present in the node and \(p\) is the distribution of the class in the node.
## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9
## [1] 10
## [1] 11
## [1] 12
## [1] 13
## [1] 14
## [1] 15
## [1] 16
## [1] 17
## [1] 18
## [1] 19
## [1] 20
## [1] 21
## [1] 22
## [1] 23
## [1] 24
## [1] 25
## [1] 26
## [1] 27
## [1] 28
## [1] 29
## [1] 30
## [1] 31
## [1] 32
## [1] 33
## [1] 34
## [1] 35
## [1] 36
## [1] 37
## [1] 38
## [1] 39
## [1] 40
## [1] 41
## [1] 42
## [1] 43
## [1] 44
## [1] 45
## [1] 46
## [1] 47
## [1] 48
## [1] 49
## [1] 50
## [1] 51
## [1] 52
## [1] 53
## [1] 54
## [1] 55
## [1] 56
## [1] 57
## [1] 58
## [1] 59
## [1] 60
## [1] 61
## [1] 62
## [1] 63
## [1] 64
## [1] 65
## [1] 66
## [1] 67
## [1] 68
## [1] 69
## [1] 70
## [1] 71
## [1] 72
## [1] 73
## [1] 74
## [1] 75
## [1] 76
## [1] 77
## [1] 78
## [1] 79
## [1] 80
## [1] 81
## [1] 82
## [1] 83
## [1] 84
## [1] 85
## [1] 86
## [1] 87
## [1] 88
## [1] 89
## [1] 90
## [1] 91
## [1] 92
## [1] 93
## [1] 94
## [1] 95
## [1] 96
## [1] 97
## [1] 98
## [1] 99
## [1] 100
| impurity | n |
|---|---|
| 0.0000000 | 41 |
| 0.1363636 | 43 |
| 0.3343109 | 1 |
| 0.3409091 | 3 |
| 0.3471074 | 11 |
| 0.3529412 | 1 |
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2435 0.3513 0.3878 0.3867 0.4193 0.5363
## # A tibble: 2 x 2
## impurity n
## <dbl> <int>
## 1 0 98
## 2 0.136 2
| item | scale | PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 | PC10 | PC11 | PC12 | PC13 | PC14 | PC15 | PC16 | PC17 | PC18 | PC19 | PC20 | PC21 | PC22 | PC23 | PC24 | PC25 | PC26 | PC27 | PC28 | PC29 | PC30 | PC31 | PC32 | PC33 | PC34 | PC35 | PC36 | PC37 | PC38 | PC39 | PC40 | PC41 | PC42 | PC43 | PC44 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SWS1 | SWS strength | -6.2 | 0.9 | -7.9 | 1.5 | -2.9 | 1.0 | -1.1 | 1.5 | -1.9 | 0.1 | 1.4 | -1.1 | 2.0 | -0.2 | -0.8 | -1.7 | 0.2 | 0.3 | 0.2 | -1.4 | -0.6 | 0.0 | 0.8 | 1.4 | 1.2 | -0.1 | -0.4 | -1.2 | 0.4 | 1.0 | 0.2 | 0.8 | -2.5 | -0.1 | 0.7 | 1.4 | 0.6 | 0.7 | 0.0 | -1.3 | 2.3 | 0.2 | -1.2 | 0 |
| SWS2 | -6.5 | 0.8 | -4.4 | -0.6 | -2.7 | -0.3 | -2.2 | 0.7 | -0.1 | 0.9 | -2.0 | -0.7 | 3.4 | -0.5 | -0.1 | -0.2 | -1.5 | -0.8 | -1.4 | 0.6 | 1.2 | -3.4 | -1.7 | 0.3 | -0.8 | 1.2 | 2.5 | 1.0 | 0.0 | -0.9 | 0.9 | -2.1 | 1.9 | 0.0 | -0.8 | -0.3 | -1.7 | 1.3 | 0.3 | -1.3 | -0.4 | -0.5 | 0.3 | 0 | |
| SWS3 | -4.7 | -0.6 | -8.2 | 1.5 | -1.8 | 1.3 | 3.1 | -2.0 | 2.9 | -0.4 | 1.3 | 0.4 | -0.4 | 0.0 | 1.4 | 2.2 | -1.1 | 1.5 | -1.2 | 0.4 | 1.7 | 0.8 | 0.1 | -1.8 | -2.6 | -0.9 | 0.5 | -2.5 | -0.3 | 1.5 | 1.1 | 1.2 | 1.0 | 0.7 | 1.1 | -1.2 | -0.3 | -0.6 | 0.6 | 1.5 | -0.5 | 0.2 | -0.4 | 0 | |
| SWS4 | -5.8 | -0.2 | -6.0 | 4.0 | -3.5 | 0.9 | -0.5 | 1.9 | -1.5 | -2.4 | -0.2 | 1.4 | 0.5 | -0.3 | 0.5 | -1.5 | 2.5 | -0.8 | 0.6 | -1.1 | 0.1 | 0.0 | 0.1 | 0.4 | 0.3 | 0.5 | -2.1 | 1.2 | -1.3 | -2.3 | -0.9 | 0.0 | -0.7 | -0.3 | 0.0 | 0.8 | 0.5 | -1.3 | -0.5 | 0.9 | -2.2 | -0.3 | 1.5 | 0 | |
| SWS29 | -0.6 | 3.0 | -3.5 | -1.5 | 8.8 | 1.3 | 3.1 | 2.2 | 0.7 | -1.2 | 3.0 | -3.3 | 1.1 | 0.7 | -0.3 | -0.5 | -2.2 | -0.7 | 1.4 | -1.7 | 0.5 | 0.3 | 1.6 | -2.5 | 1.4 | -1.5 | 0.2 | 1.4 | -1.9 | -1.2 | 0.5 | -1.2 | 0.7 | -0.1 | -1.2 | 0.5 | -0.1 | 0.1 | -0.4 | 0.5 | 0.3 | 0.3 | -0.2 | 0 | |
| SWS35 | 0.1 | 5.2 | -2.8 | -0.3 | 2.7 | -0.4 | 1.1 | 0.7 | 1.8 | -0.3 | -1.6 | -1.4 | 1.3 | -3.7 | -1.7 | 0.7 | 0.4 | -3.0 | 3.5 | 1.4 | -0.2 | 1.3 | -3.0 | 1.3 | -1.2 | 0.4 | -1.3 | 2.4 | 2.0 | 1.5 | -1.1 | 1.1 | 0.9 | -0.6 | 0.5 | -0.8 | 0.9 | -0.3 | 1.1 | -0.1 | 0.2 | 0.4 | 0.0 | 0 | |
| SWS5 | SWS emotion | 0.1 | -5.1 | -1.6 | 3.7 | 0.5 | -2.9 | -4.4 | -2.3 | 3.7 | 2.0 | 3.5 | 0.8 | 1.1 | 2.4 | 0.5 | 1.3 | -1.0 | 0.5 | 0.6 | 0.6 | -2.5 | 0.3 | 1.5 | -0.2 | 1.2 | 0.9 | 0.0 | 0.9 | 1.6 | -0.4 | -0.6 | -1.1 | 1.4 | -2.3 | 1.7 | -0.3 | 0.0 | -0.9 | -0.8 | -0.1 | 0.6 | 1.0 | 0.6 | 0 |
| SWS6 | 3.3 | -8.1 | -1.3 | 2.7 | 1.1 | -2.7 | -3.0 | 1.1 | 1.4 | 1.3 | 0.2 | 0.6 | 1.2 | 1.2 | 0.2 | 0.7 | 1.0 | -0.4 | 0.6 | 3.5 | 1.0 | 2.2 | -1.3 | 0.9 | 0.6 | 0.6 | -0.8 | -0.7 | -1.5 | 0.2 | 1.4 | 0.1 | -0.2 | -0.2 | -3.6 | 0.4 | 0.8 | 0.1 | 0.7 | 0.7 | 0.2 | -0.9 | -0.9 | 0 | |
| SWS7 | 5.0 | -3.7 | -0.3 | 0.2 | 4.1 | -0.3 | 6.4 | 0.7 | -1.2 | -3.2 | 0.4 | 4.3 | 1.7 | 0.7 | 0.1 | 2.2 | 2.0 | -0.6 | -2.9 | -2.6 | -1.7 | -2.2 | -0.2 | 1.4 | 0.1 | 2.5 | 0.5 | -0.1 | 0.7 | 1.2 | 0.2 | 0.8 | 0.9 | -0.9 | -0.5 | 0.6 | 0.4 | -0.2 | -0.2 | -0.3 | -0.1 | -0.4 | -0.5 | 0 | |
| SWS8 | 6.6 | -6.1 | 0.7 | 1.9 | 0.3 | -1.4 | 1.2 | 1.7 | -0.9 | -0.5 | -1.5 | 0.2 | -0.1 | -2.8 | 1.1 | -0.2 | -0.4 | 0.1 | 1.1 | 0.8 | 2.5 | -1.1 | 1.0 | -2.1 | -2.7 | 0.8 | 0.2 | 1.2 | 0.1 | -1.6 | 1.4 | 0.9 | -0.7 | 1.0 | 0.8 | -1.0 | 1.1 | -0.5 | -1.8 | -0.7 | 2.0 | -0.5 | 0.9 | 0 | |
| SWS9 | 5.9 | -6.7 | 1.3 | 1.7 | 1.1 | -2.7 | 0.6 | 1.5 | -1.2 | 0.3 | -1.0 | 0.1 | 0.8 | -0.5 | -0.5 | -0.3 | 0.1 | 1.3 | 1.8 | 0.4 | 0.9 | -2.7 | 0.3 | 0.0 | -1.7 | -2.2 | -0.4 | -0.7 | -0.3 | -1.1 | -2.0 | 1.0 | -0.4 | -0.3 | 0.4 | 1.1 | -1.3 | 0.9 | 1.3 | -0.1 | -1.0 | 2.5 | -0.9 | 0 | |
| SWS10 | 6.4 | -6.5 | 0.3 | 1.7 | -0.5 | -1.1 | 1.4 | 0.7 | -4.2 | -0.9 | -0.7 | -0.2 | 1.2 | -0.7 | -1.3 | -1.7 | -0.5 | 0.5 | 1.7 | -1.4 | -0.6 | 1.7 | -2.2 | 0.0 | 3.1 | -1.9 | 1.7 | -0.9 | 0.6 | 0.1 | 0.7 | -1.7 | 0.2 | 0.0 | 2.3 | -1.5 | -0.1 | 0.4 | 0.9 | 1.0 | -0.3 | -1.4 | 0.1 | 0 | |
| SWS30 | 6.1 | -2.3 | -0.6 | 3.2 | 2.2 | -0.6 | -1.1 | 2.0 | 0.9 | 0.6 | -0.5 | -2.7 | -1.5 | -0.9 | -0.6 | 0.1 | -1.1 | -1.4 | -3.5 | 0.5 | -2.6 | 1.5 | 1.1 | -1.6 | -0.7 | 0.1 | -2.9 | -0.1 | 0.1 | 1.8 | 0.2 | -0.1 | -0.4 | 1.4 | 0.9 | 0.8 | -1.4 | 1.0 | 0.1 | -1.6 | -1.3 | -1.1 | 0.6 | 0 | |
| SWS11 | SWS vulnerable | 5.4 | -3.2 | -1.1 | -2.6 | -3.3 | 2.7 | 0.3 | -2.4 | 1.4 | -2.4 | -2.3 | -1.7 | -0.5 | -2.4 | -2.1 | -3.1 | -1.8 | 2.9 | 1.2 | 0.2 | -4.7 | 0.3 | 1.1 | 0.9 | -1.1 | 0.3 | 1.7 | 0.2 | -0.8 | 0.9 | -0.4 | -0.2 | 1.0 | 0.8 | -1.7 | 0.8 | 0.4 | -1.0 | -0.7 | 0.3 | 0.0 | 0.5 | 0.1 | 0 |
| SWS12 | 4.3 | -0.3 | 0.1 | -4.1 | 2.4 | 3.9 | -1.4 | -0.6 | 3.2 | -0.9 | -4.2 | -0.2 | 4.1 | 0.8 | 3.8 | -0.6 | -2.0 | 2.8 | -2.3 | 0.6 | 1.5 | -0.4 | -0.2 | 0.0 | 1.8 | 0.4 | -1.2 | 0.2 | 0.6 | 0.2 | -1.9 | -0.3 | -2.3 | -0.5 | 0.3 | -1.1 | 0.4 | -0.5 | 0.3 | 0.2 | -0.2 | -0.2 | 0.1 | 0 | |
| SWS13 | 6.2 | -1.3 | -0.9 | -3.1 | -5.1 | 0.2 | 1.6 | 0.5 | 2.0 | 0.2 | 1.6 | -1.6 | -2.3 | 2.2 | -0.6 | 1.0 | 1.1 | -2.8 | 1.0 | 0.6 | 0.5 | -0.9 | -1.5 | -2.5 | 0.8 | 0.0 | 1.5 | 0.7 | 0.4 | 0.4 | -2.8 | 0.5 | -1.1 | -0.6 | -0.3 | 0.1 | -0.9 | -0.2 | -2.0 | 0.1 | -0.4 | -1.1 | -1.3 | 0 | |
| SWS14 | 6.5 | -1.5 | -0.4 | -4.2 | -3.3 | 2.3 | 0.6 | -0.3 | 2.9 | 0.8 | 0.6 | -0.5 | -3.2 | 1.5 | -1.0 | 0.6 | 1.5 | -1.2 | 0.7 | -2.0 | -0.3 | -1.4 | -0.7 | -1.9 | 1.0 | 1.4 | -0.5 | 0.0 | -0.3 | -0.5 | 2.3 | -0.7 | -1.2 | -0.1 | -0.4 | -0.5 | 0.7 | 0.0 | 2.8 | -0.7 | 0.3 | 1.2 | 1.0 | 0 | |
| SWS15 | 6.1 | -0.7 | -0.7 | -3.2 | -2.2 | 0.6 | 1.7 | -3.2 | 0.7 | 1.0 | -0.8 | -2.8 | -1.6 | 1.6 | 1.5 | 0.6 | 0.5 | 1.2 | 0.5 | -1.5 | 2.2 | 0.1 | 0.0 | 4.2 | 1.0 | -1.3 | -3.1 | 0.8 | 0.0 | -1.0 | 1.5 | 1.0 | 2.3 | -0.1 | 0.5 | 0.8 | -0.8 | 0.7 | -1.0 | -0.1 | 0.3 | -0.4 | 0.0 | 0 | |
| SWS16 | 1.9 | 1.0 | -0.3 | -3.7 | -0.8 | -1.9 | -3.6 | 4.7 | -1.1 | 1.2 | 0.5 | 0.6 | -2.1 | 0.6 | 2.6 | -0.5 | 0.6 | 0.5 | 0.9 | -1.6 | 1.3 | -0.6 | 3.2 | 0.5 | -1.4 | 0.3 | 0.8 | 0.5 | -0.6 | 2.4 | -2.1 | -0.6 | 1.6 | 0.0 | 0.4 | 0.5 | 1.6 | 1.0 | 1.2 | 0.9 | 0.2 | -1.1 | 0.4 | 0 | |
| SWS31 | 2.9 | 1.5 | 0.0 | -4.5 | 1.1 | -0.1 | -3.8 | -1.1 | -0.1 | -0.6 | -1.3 | 0.8 | 2.0 | 1.6 | -2.1 | -3.3 | 1.4 | -5.2 | -2.7 | 0.2 | -0.5 | -0.2 | 1.8 | 0.0 | -1.3 | -2.8 | 0.4 | -1.9 | 0.9 | -1.0 | 1.1 | 1.4 | 0.5 | -0.9 | 0.0 | -0.9 | 0.8 | 0.0 | -0.5 | 0.5 | -0.2 | 0.2 | 0.0 | 0 | |
| SWS17 | SWS succeed | 1.1 | 0.9 | -0.8 | -4.3 | 2.6 | -0.3 | -2.8 | 1.0 | 1.6 | -4.7 | 3.1 | 2.6 | -3.2 | -4.0 | 2.2 | -0.1 | -0.2 | -0.8 | 0.9 | 0.8 | 1.0 | 1.2 | -1.3 | 1.6 | 0.9 | 1.0 | 0.6 | -3.3 | 0.8 | -1.0 | -0.4 | -1.1 | -0.2 | 0.6 | 0.1 | 0.4 | -1.0 | 0.5 | -0.8 | -0.6 | -0.1 | 0.6 | 0.4 | 0 |
| SWS18 | -0.4 | 2.4 | -0.5 | -2.5 | 0.1 | -1.5 | -3.5 | 0.1 | -2.3 | 0.2 | 0.3 | 1.7 | -0.9 | -1.8 | 2.6 | 5.0 | -0.3 | 0.0 | 0.0 | 0.6 | -3.3 | -1.9 | -0.4 | 1.0 | 0.9 | -2.9 | 0.5 | 2.2 | -2.3 | 0.6 | 1.5 | 0.9 | -1.3 | 0.4 | 0.2 | -1.2 | -0.1 | -0.3 | -0.5 | 0.1 | -0.3 | 0.2 | -0.3 | 0 | |
| SWS19 | 4.5 | 3.0 | -0.6 | 1.1 | 0.3 | -2.7 | 3.2 | -4.2 | -1.0 | 4.8 | 0.0 | 0.1 | 1.1 | -0.8 | 3.0 | -2.1 | 1.9 | -1.3 | -1.1 | 0.3 | 1.5 | 2.4 | -0.2 | 0.1 | 1.5 | 0.1 | 2.9 | 0.4 | -1.4 | 1.5 | -0.4 | 0.4 | -0.4 | 0.6 | -0.1 | 0.9 | 0.5 | 0.1 | -0.5 | -0.9 | -0.6 | 1.4 | 1.1 | 0 | |
| SWS20 | 2.3 | 4.8 | 0.5 | -0.3 | 0.5 | -4.6 | 0.5 | -5.3 | -1.8 | 1.7 | 2.8 | -0.9 | -0.7 | -3.5 | 0.8 | -2.9 | 0.2 | 0.2 | -1.5 | 1.0 | -0.7 | -2.4 | 0.8 | -0.5 | 0.1 | 2.0 | -1.4 | 0.1 | 0.0 | -1.6 | -0.4 | -0.5 | -0.3 | 0.3 | 0.2 | -0.1 | -0.5 | -1.1 | 1.4 | 1.2 | 0.4 | -1.1 | -1.2 | 0 | |
| SWS32 | 1.2 | 2.5 | -0.2 | -1.5 | 2.5 | -0.1 | -1.8 | -1.3 | -1.3 | 5.0 | -2.7 | 2.1 | 0.9 | 1.6 | -2.8 | 2.1 | -1.4 | -0.4 | 2.3 | -3.3 | -0.6 | 0.8 | -1.4 | 0.2 | -1.7 | 1.7 | -1.1 | -2.7 | -2.4 | -0.6 | -1.4 | -0.5 | -0.2 | 0.7 | 0.2 | -0.4 | -0.6 | -0.9 | -0.7 | -0.2 | 0.4 | -0.3 | 0.1 | 0 | |
| SWS33 | 1.4 | 3.0 | -2.7 | -2.4 | 1.8 | -3.3 | -2.4 | -2.8 | -4.7 | -2.3 | 1.5 | 0.9 | -2.0 | 3.0 | -4.6 | 0.2 | -1.8 | 4.1 | -0.9 | 0.9 | 2.2 | 0.2 | -1.0 | -1.0 | 0.0 | 0.2 | 0.0 | 1.2 | 1.5 | 0.7 | -0.1 | 1.2 | -0.5 | -0.1 | -0.8 | -0.1 | 0.6 | 0.2 | -0.2 | -0.7 | -0.7 | 0.1 | 0.7 | 0 | |
| SWS21 | SWS care | 3.3 | 5.7 | 1.2 | 2.1 | -1.7 | 0.6 | 2.9 | -1.0 | 0.5 | 0.5 | 0.6 | 3.3 | -0.5 | 0.9 | 1.9 | -1.5 | -1.4 | 1.0 | 0.7 | -0.2 | -1.8 | 1.4 | -1.1 | -0.3 | -3.5 | -0.9 | -0.8 | 0.6 | 0.5 | -0.6 | 0.9 | -2.0 | -1.5 | -2.2 | -0.5 | 0.1 | 0.4 | 2.7 | -0.6 | 0.5 | -0.1 | -0.2 | -0.1 | 0 |
| SWS22 | 3.1 | 5.0 | 3.3 | 3.9 | -1.5 | 2.2 | -1.2 | 0.5 | 1.5 | -0.2 | 2.2 | 4.3 | 2.1 | 1.7 | 1.9 | -1.8 | -0.5 | 0.7 | 2.7 | -1.2 | 0.0 | -0.2 | 0.1 | -1.1 | 0.6 | -1.9 | -0.1 | 0.3 | 1.7 | 0.0 | 0.2 | 1.5 | 1.1 | 2.2 | -1.1 | 0.1 | -0.8 | -1.3 | 0.8 | -1.5 | -0.1 | -0.9 | -0.3 | 0 | |
| SWS23 | 4.2 | 6.2 | 3.4 | 3.6 | -1.0 | 1.0 | -1.0 | 2.2 | 0.2 | -0.9 | -0.3 | -2.4 | -0.4 | -0.5 | -0.6 | 0.7 | 0.7 | 1.6 | -0.2 | 0.8 | 1.2 | -0.6 | 0.1 | -0.1 | 0.3 | 0.6 | 0.0 | -1.6 | -1.3 | 0.0 | 1.1 | -1.4 | 1.1 | -1.1 | 1.0 | -0.5 | 2.4 | -1.0 | -0.7 | -1.6 | -1.5 | 0.5 | -1.6 | 0 | |
| SWS24 | 3.3 | 6.4 | 2.2 | 5.3 | -0.4 | 0.7 | -0.1 | 2.5 | 1.4 | 0.2 | 0.6 | -1.2 | 0.6 | -0.9 | -2.4 | -0.5 | 2.6 | 1.7 | -0.2 | 0.7 | 0.0 | -2.4 | 0.3 | 0.3 | 1.9 | 0.5 | -0.4 | -1.5 | -0.7 | 1.4 | -0.2 | 1.1 | 0.1 | -0.5 | -1.0 | -1.8 | -1.4 | 1.3 | -0.9 | 1.5 | 1.0 | 0.4 | 1.4 | 0 | |
| SWS25 | 4.4 | 3.7 | 0.7 | 2.3 | -1.2 | 1.0 | 1.8 | 3.8 | -3.0 | -0.7 | 0.8 | -3.3 | -1.2 | 3.4 | 1.4 | 1.6 | -1.6 | -0.6 | -2.1 | 1.5 | -1.0 | 2.4 | 0.3 | 3.0 | -1.6 | 0.5 | 2.0 | -0.1 | 0.4 | -2.2 | -1.0 | 0.4 | -0.4 | 0.0 | -0.3 | -0.8 | -0.9 | -1.3 | 1.2 | 0.0 | 0.9 | 0.3 | 0.4 | 0 | |
| SWS34 | 4.6 | 4.6 | 1.8 | 2.2 | -0.9 | 2.2 | -1.8 | -0.8 | 0.7 | -2.0 | -3.2 | 2.7 | 0.3 | 0.3 | -2.6 | 2.4 | -0.3 | -1.2 | -0.7 | 1.7 | 1.5 | 0.7 | 0.8 | -0.7 | 0.9 | 0.5 | 0.9 | 1.3 | -0.2 | 0.0 | 1.0 | -1.0 | -0.1 | 0.9 | 1.6 | 3.4 | -0.6 | -0.1 | 0.3 | 1.7 | 0.8 | 0.3 | -0.3 | 0 | |
| JH_1 | JH | -7.4 | -1.5 | 4.7 | -1.1 | -3.9 | -1.1 | 2.7 | -0.6 | -2.6 | -3.0 | 1.0 | 0.5 | 1.3 | 2.4 | 1.1 | -0.9 | -4.5 | -3.2 | 0.4 | 2.0 | -0.2 | -0.6 | -0.5 | -0.6 | 1.2 | 1.1 | -2.6 | -0.5 | -1.7 | 1.4 | -0.6 | -0.1 | 1.0 | 1.1 | 0.2 | -0.6 | 0.8 | 0.6 | -0.2 | 0.2 | 0.5 | 1.1 | 0.2 | 0 |
| JH_2 | -8.3 | -0.6 | 2.3 | -0.8 | -0.9 | -2.2 | 1.3 | -1.0 | 0.8 | -2.7 | -3.1 | 1.9 | -1.6 | -0.9 | -0.9 | -1.0 | 0.8 | 0.1 | 0.7 | -0.4 | 1.3 | 2.6 | 3.1 | -0.3 | 0.2 | -0.1 | 0.1 | 0.9 | -1.8 | 0.8 | 0.1 | 0.1 | -0.2 | -2.7 | -0.1 | -1.3 | -2.3 | -0.8 | 0.8 | -1.3 | 0.4 | -0.4 | -0.4 | 0 | |
| JH_3 | -7.8 | 0.5 | 2.1 | 0.2 | 0.7 | -3.6 | 1.9 | -1.5 | 5.0 | -1.2 | -0.3 | -0.5 | 0.8 | 1.4 | -2.1 | 1.4 | 0.7 | 0.7 | 1.0 | 0.0 | -1.0 | 0.5 | 1.9 | 1.5 | 0.6 | 0.8 | 1.6 | 0.3 | -0.3 | -2.3 | -0.6 | 1.2 | -0.9 | 2.3 | 0.9 | -0.7 | 1.3 | 2.2 | 0.3 | -0.3 | -0.8 | -0.8 | -0.2 | 0 | |
| JH_4 | -6.9 | -0.2 | 2.8 | 1.4 | -0.8 | -4.4 | 1.7 | -1.4 | 2.2 | -1.4 | -0.5 | -1.7 | -0.3 | -0.3 | -0.8 | 1.9 | 1.4 | 0.2 | -2.0 | -1.3 | 0.7 | -1.0 | -1.4 | 0.4 | -0.9 | -3.9 | -0.6 | -0.9 | 0.9 | 0.7 | -1.3 | -2.9 | -0.5 | 0.6 | -1.1 | 1.0 | 0.8 | -1.4 | 0.0 | -0.2 | 1.1 | -0.3 | 0.8 | 0 | |
| JH_5 | -5.3 | 0.1 | 1.8 | -2.1 | -1.5 | -3.5 | 1.1 | 4.5 | -0.2 | 3.3 | -1.4 | -0.1 | -0.2 | -0.7 | -0.2 | -0.1 | -1.7 | -0.1 | 0.2 | -2.0 | 0.5 | 0.7 | 1.6 | 0.6 | 0.7 | 1.3 | -0.3 | 0.4 | 3.4 | 0.6 | 2.0 | -0.7 | -1.1 | 1.0 | -1.0 | -0.4 | -0.6 | -0.9 | -1.1 | 1.3 | -1.2 | 1.2 | -0.7 | 0 | |
| JH_6 | -8.0 | 0.6 | 3.8 | -2.4 | -0.3 | -1.0 | 1.2 | 2.8 | 0.8 | 2.5 | -0.7 | -0.9 | -0.2 | -1.7 | 0.7 | 0.1 | -2.4 | 1.4 | -0.3 | 0.5 | -1.2 | -0.2 | -2.0 | -1.8 | 1.0 | -0.2 | 0.8 | -1.6 | 0.0 | -1.0 | 0.7 | 3.1 | 0.5 | -2.4 | 0.4 | 2.5 | 0.5 | -0.3 | 0.4 | 0.1 | -0.1 | -1.0 | 0.9 | 0 | |
| JH_7 | -5.3 | -3.7 | -0.2 | 1.6 | 1.7 | 6.7 | 2.7 | 0.4 | 0.1 | 5.1 | 1.0 | 3.7 | -4.2 | -1.7 | -3.0 | -0.8 | -1.9 | -0.6 | -1.6 | 2.2 | 1.1 | -1.2 | 0.9 | 1.9 | 1.3 | -1.4 | 0.0 | 0.6 | 0.2 | -0.4 | -1.1 | -0.6 | 0.1 | 0.1 | -0.1 | -0.6 | 0.8 | -0.1 | 0.1 | -0.4 | 0.0 | -0.3 | -0.1 | 0 | |
| JH_8 | -7.1 | -1.2 | 1.0 | -2.2 | 1.3 | 0.3 | -1.3 | 3.2 | 0.4 | 0.6 | -0.6 | 1.2 | -1.6 | 1.5 | 0.5 | -2.9 | 4.0 | 2.5 | -3.0 | -0.2 | -1.3 | 1.9 | -3.4 | -1.6 | -0.4 | 0.2 | -0.6 | 1.7 | -0.7 | -0.8 | -0.3 | 0.0 | 1.5 | 1.4 | 0.9 | -0.5 | -0.2 | 0.1 | -0.3 | 0.3 | 1.0 | 1.0 | -0.9 | 0 | |
| JH_9 | -7.9 | -2.2 | 2.9 | -0.1 | 5.0 | 2.7 | -0.4 | -1.5 | -0.3 | -0.2 | 0.7 | -2.1 | -0.9 | 3.7 | 1.1 | -2.5 | 2.1 | -0.1 | 3.0 | 1.9 | -0.1 | -2.3 | -0.6 | 1.7 | -2.0 | 0.8 | 0.9 | -0.2 | 0.0 | 2.0 | 1.7 | -0.4 | -1.5 | 0.2 | 1.2 | 0.7 | -0.8 | -0.9 | -0.3 | 0.2 | -0.5 | -0.5 | 0.3 | 0 | |
| JH_10 | -2.7 | -2.1 | 3.8 | -5.7 | -2.2 | 4.6 | 0.8 | -0.6 | -3.1 | 1.3 | 4.4 | -0.9 | 5.2 | -2.2 | -1.3 | 3.2 | 3.5 | 1.4 | 0.3 | 1.5 | 0.1 | 2.0 | 1.7 | -1.0 | -1.1 | 0.1 | -0.8 | -0.1 | 0.6 | -0.2 | -0.2 | -0.8 | 0.1 | 0.0 | -0.1 | 0.1 | -0.3 | 0.3 | 0.1 | -0.2 | -0.3 | -0.1 | 0.3 | 0 | |
| JH_11 | -3.3 | -4.0 | 5.3 | 4.6 | 0.0 | 3.6 | -5.0 | -3.2 | 0.0 | -1.3 | 2.5 | -2.3 | -0.4 | -2.2 | 0.1 | 0.3 | -1.7 | -1.4 | -1.7 | -4.8 | 1.8 | 0.8 | -1.4 | 0.5 | -1.1 | 0.8 | 1.0 | 1.3 | -0.3 | 0.4 | -0.3 | 1.3 | -0.5 | -0.4 | -0.6 | -0.2 | 0.2 | 0.6 | 0.1 | 0.7 | -0.2 | 0.3 | -0.4 | 0 | |
| JH_12 | -6.1 | 0.1 | -1.2 | 3.2 | 1.8 | 2.8 | -0.8 | -3.6 | -4.2 | -0.3 | -5.0 | -1.7 | -2.9 | 0.5 | 3.1 | 2.3 | 2.0 | -0.5 | 1.5 | 0.3 | -1.4 | -0.1 | 1.2 | -2.5 | 1.3 | 0.3 | -0.1 | -1.3 | 2.4 | -0.8 | -0.7 | 0.0 | 1.0 | 0.0 | -1.3 | -0.2 | 0.4 | 1.0 | 0.0 | 0.0 | 0.2 | 0.2 | -0.3 | 0 |
When the data is not centered and scaled, JH dominates on account of it containing more room for variance than the SWS items.
| Subject_Number | SWS1 | SWS2 | SWS3 | SWS4 | SWS29 | SWS35 | SWS5 | SWS6 | SWS7 | SWS8 | SWS9 | SWS10 | SWS30 | SWS11 | SWS12 | SWS13 | SWS14 | SWS15 | SWS16 | SWS31 | SWS17 | SWS18 | SWS19 | SWS20 | SWS32 | SWS33 | SWS21 | SWS22 | SWS23 | SWS24 | SWS25 | SWS34 | JH_1 | JH_2 | JH_3 | JH_4 | JH_5 | JH_6 | JH_7 | JH_8 | JH_9 | JH_10 | JH_11 | JH_12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1001 | 4 | 4 | 4 | 4 | 3 | 4 | 3 | 3 | 1 | 3 | 3 | 1 | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 4 | 4 | 2 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | 2 | 5 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 2 | 1 | 5 |
| 1002 | 3 | 3 | 4 | 4 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 3 | 2 | 3 | 3 | 2 | 2 | 3 | 2 | 4 | 1 | 3 | 4 | 4 | 3 | 4 | 3 | 3 | 3 | 4 | 5 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 |
| 1003 | 4 | 4 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 4 | 4 | 4 | 4 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 4 | 4 | 5 | 4 | 4 | 5 | 2 | 4 | 5 | 4 |
| 1004 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 2 | 1 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 |
| 1005 | 3 | 3 | 3 | 3 | 2 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 2 | 2 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 2 | 5 | 4 | 4 | 4 | 5 | 4 | 4 |